ZOOM Number Theory Seminar

This seminar is held on ZOOM and organized by Morningside Center of Mathematics (MCM) and Yau Mathematical Sciences Center (YMSC).

Organizers

Hansheng Diao (YMSC)

Lei Fu (YMSC)

Yongquan Hu (MCM)

Ye Tian (MCM)

Bin Xu (YMSC)

Weizhe Zheng (MCM)

Conference Room for the current talk

Sechdule

Title: TBA

Speaker: Prof. Yifeng Liu (Yale)

Time: 16:00-17:00, July 23, 2020 (Beijing Time)

Abstract: TB

Title: Bound on the number of rational points on curves

Speaker: Prof. Ziyang Gao (CNRS)

Time: 16:00-17:00, July 9, 2020 (Beijing Time)

Abstract: Mazur conjectured, after Faltings's proof of the Mordell conjecture, that the number of rational points on a curve depends only on the genus, the degree of the number field and the Mordell-Weil rank. This conjecture was established in a few cases. In this talk I will explain how to prove this conjecture and some of its generalization. I will focus on how functional transcendence and unlikely intersections on mixed Shimura varieties are applied. This is joint work with Vesselin Dimitrov and Philipp Habegger.

Title: Towards three problems of Katz on Kloosterman sums

Speaker: Prof. Ping Xi (Xi'an Jiaotong University )

Time: 16:00-17:00, June 24, 2020 (Beijing Time)

Abstract: Motivated by deep observations on elliptic curves, Nicholas Katz proposed three problems on sign changes, equidistributions and modular structures of Kloosterman sums in 1980. In this talk, we will discuss some recent progresses towards these three problems made by analytic number theory combining certain tools from $\ell$-adic cohomology.

Title: Algebraic cycles on Shimura varieties and L-functions

Speaker: Prof. Wei Zhang (MIT)

Time: 9:30-11:00, June 11, 2020 (Beijing Time)

Abstract: This will be an introductory talk to special algebraic cycles on Shimura varieties and their relation to L-functions. No prior knowledge Shimura varieties will be assumed.

PPT & Video

Title: The arithmetic fundamental lemma for p-adic fields

Speaker: Prof. Wei Zhang (MIT)

Time: 9:00-10:30, June 4, 2020 (Beijing Time)

Abstract: The arithmetic fundamental lemma (AFL) is a conjectural identity relating the arithmetic intersection numbers on a Rapoport-Zink space for unitary groups to the first derivative of relative orbital integral on the general linear groups over a p-adic field F. The AFL was proved in the case F=Q_p about one year ago. In this talk I will report a work in progress joint with A. Mihatsch to prove the AFL for a general p-adic field.

PPT & Video